A two-parameter family of double-power-law biorthonormal potential-density expansions
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Abstract
Biorthonormal basis function expansions are widely used in galactic dynamics,
both to study problems in galactic stability and to provide numerical
algorithms to evolve collisionless stellar systems. They also provide a compact
and efficient description of the structure of numerical dark matter haloes in
cosmological simulations. We present a two-parameter family of biorthonormal
double-power-law potential-density expansions. Both the potential and density
are given in closed analytic form and may be rapidly computed via recurrence
relations. We show that this family encompasses all the known analytic
biorthonormal expansions: the Zhao expansions (themselves generalizations of
ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the
recently discovered Lilley, Sanders, Evans & Erkal expansion. Our new
two-parameter family includes expansions based around many familiar spherical
density profiles as zeroth-order models, including the
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1365-2966
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Science and Technology Facilities Council (1788901)